Skip to main content

1984 | OriginalPaper | Buchkapitel

The Exact Computation of the Characteristic Polynomial of a Matrix

verfasst von : R. T. Gregory, E. V. Krishnamurthy

Erschienen in: Methods and Applications of Error-Free Computation

Verlag: Springer New York

Aktivieren Sie unsere intelligente Suche um passende Fachinhalte oder Patente zu finden.

search-config
loading …

It is not recommended, in general, that we compute the coefficients of the characteristic polynomial of a matrix as a first step in finding the eigenvalues of the matrix by polynomial root-finding techniques. This is due to the fact that if ordinary floating-point arithmetic is used, the accumulation of rounding errors will produce only approximations to the coefficients and, if the polynomial is ill-conditioned, the roots of the “approximate characteristic equation” may not be good approximations to the roots of the characteristic equation. See Wilkinson [1963], Chapter 2, for a discussion of the condition of a polynomial equation with respect to the computation of its roots.

Metadaten
Titel
The Exact Computation of the Characteristic Polynomial of a Matrix
verfasst von
R. T. Gregory
E. V. Krishnamurthy
Copyright-Jahr
1984
Verlag
Springer New York
DOI
https://doi.org/10.1007/978-1-4612-5242-9_6